Iterative version of the QRD for adaptive recursive least squares (RLS) filtering

Juergen Goetze

doi:10.1117/12.190856

28 October 1994 Iterative version of the QRD for adaptive recursive least squares (RLS) filtering

Juergen Goetze

Proceedings Volume 2296, Advanced Signal Processing: Algorithms, Architectures, and Implementations V; (1994) https://doi.org/10.1117/12.190856
Event: SPIE's 1994 International Symposium on Optics, Imaging, and Instrumentation, 1994, San Diego, CA, United States

Abstract

A modified version of the QR-decomposition (QRD) is presented. It uses approximate Givens rotations instead of exact Givens rotations, i.e., a matrix entry usually annihilated with an exact rotation by an angle (sigma) is only reduced by using an approximate rotation by an angle (sigma) . The approximation of the rotations is based on the idea of CORDIC. Evaluating a CORDIC-based approximate rotation is to determine the angle (sigma) equals (sigma) _t equals arctan 2^-t, which is closest to the exact rotation angle (sigma) . This angle (sigma) _t is applied instead of (sigma) . Using approximate rotations for computing the QRD results in an iterative version of the original QRD. A recursive version of this QRD using CORDIC-based approximate rotations is applied to adaptive RLS filtering. Only a few angles of the CORDIC sequence, r say (r << b, where b is the word length), work as well as using exact rotations (r equals b, original CORDIC). The misadjustment error decreases as r increases. The convergence of the QRD-RLS algorithm, however, is insensitive to the value of r. Adapting the approximation accuracy during the course of the QRD-RLS algorithm is also discussed. Simulations (channel equalization) confirm the results.

Citation Download Citation

Juergen Goetze "Iterative version of the QRD for adaptive recursive least squares (RLS) filtering", Proc. SPIE 2296, Advanced Signal Processing: Algorithms, Architectures, and Implementations V, (28 October 1994); https://doi.org/10.1117/12.190856

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